# Phillips Curve - Mathematics and The Phillips Curve - New Classical Version

New Classical Version

The Phillips curve equation can be derived from the (short-run) Lucas aggregate supply function. The Lucas approach is very different from that the traditional view. Instead of starting with empirical data, he started with a classical economic model following very simple economic principles.

where Y is log value of the actual output, Yn is log value of the "natural" level of output, a is a positive constant, P is log value of the actual price level, and Pe is log value of the expected price level. Lucas assumes that Yn has a unique value.

Note that this equation indicates that when expectations of future inflation (or, more correctly, the future price level) are totally accurate, the last term drops out, so that actual output equals the so-called "natural" level of real GDP. This means that in the Lucas aggregate supply curve, the only reason why actual real GDP should deviate from potential—and the actual unemployment rate should deviate from the "natural" rate—is because of incorrect expectations of what is going to happen with prices in the future. (The idea has been expressed first by Keynes, "General Theory," Chapter 20 section III paragraph 4).

This differs from other views of the Phillips curve, in which the failure to attain the "natural" level of output can be due to the imperfection or incompleteness of markets, the stickiness of prices, and the like. In the non-Lucas view, incorrect expectations can contribute to aggregate demand failure, but they are not the only cause. To the "new Classical" followers of Lucas, markets are presumed to be perfect and always attain equilibrium (given inflationary expectations).

We re-arrange the equation into:

Next we add unexpected exogenous shocks to the world supply v:

Subtracting last year's price levels P-1 will give us inflation rates, because

and

where π and πe are the inflation and expected inflation respectively.

There is also a negative relationship between output and unemployment (as expressed by Okun's law). Therefore using

where b is a positive constant, U is unemployment, and Un is the natural rate of unemployment or NAIRU, we arrive at the final form of the short-run Phillips curve:

This equation, plotting inflation rate π against unemployment U gives the downward-sloping curve in the diagram that characterises the Phillips curve.

### Other articles related to "classical, versions, version":

Natural Killer Cell - NK Cell Receptors - Activating Receptors
... presence in mice, while humans have only one pseudogenic Ly49 the receptor for classical (polymorphic) MHC I molecules ... conserved in both rodents and primates and identifies non-classical (also non-polymorphic) MHC I molecules like HLA-E ... on the presence of nonamer peptide epitope derived from the signal sequence of classical MHC class I molecules, which is generated by the sequential action of signal peptide ...
Kishori Amonkar
... आमोणकर) (born 10 April 1931) is an Indian singer who performs in the classical genre khyal and the light classical genres thumri and bhajan ... Amonkar trained under her mother, classical singer Mogubai Kurdikar of the Jaipur gharana (musical tradition of Jaipur), but experimented with a variety of vocal styles in her career ... preeminent representatives of Hindustani classical music ...
Cor Anglais - Use Outside Classical Music
... Though primarily featured in classical music, the cor anglais has also been used by a few musicians as a jazz instrument most prominent among these ... Judy Collins' and Barbra Streisand's) versions of Send in the Clowns ... soap opera Emmerdale Farm was originally performed on the cor anglais, as was also the version of Harry South's theme tune played at the end of each episode of The ...
Foot (prosody) - The Poetic Feet in Classical Meter
... Below are listed the names given to the poetic feet by classical metrics ... three, and tetrasyllables four) and secondarily by the pattern of vowel lengths (in classical languages) or syllable stresses (in English poetry) which ... The following lists describe the feet in terms of vowel length (as in classical languages) ...

### Famous quotes containing the words version and/or classical:

Exercise is the yuppie version of bulimia.
Barbara Ehrenreich (b. 1941)

Against classical philosophy: thinking about eternity or the immensity of the universe does not lessen my unhappiness.
Mason Cooley (b. 1927)